In chapter one, some new formulas for Caputo fractional derivatives of some elementary functions is given. The system of M-linear Voltera integro-fractional differential equations is reduced into a system of Voltera integral equations and the global and semi-global fundamental existence and uniquenas theorems and presented in Chapter two. In chapter three, some analytic and approximate methods are applied to treat such a system. In chapter four, Runge-Kutta methods with different orders are given to treat such a system. The convergence and stability are also investigated. In chapter five, special Chebyshev method is considered. In chapter six, conclusions and recommendations with comparisons between the methods are included.

Autorentext

Suha Najeeb ShihabAuthors C.V. suha N. Al-Rawi received her B.Sc. degree in Applied Mathematics from University of Technology in 1992, and her M.Sc. in Applied Mathematics from University of Technology in 1995, and her Ph.D. in Mathematics from Al-Mustansiriya University in 2005. Her areas of specially include control theory and Integral Equations